Global Continuation and Asymptot ic Behaviour for Periodic Solutions of a Differential-Delay Equation ( * )

@inproceedings{JS2005GlobalCA,
title={Global Continuation and Asymptot ic Behaviour for Periodic Solutions of a Differential-Delay Equation ( * )},
author={R JS and Roger and I Hussbau},
year={2005}
}

The singularly perturbed di]#rentiat.delay equation ~(t) =-x(t) + l(x(t-1)) is studied. Existence o] periodic solutions is shown using a global continuation technique based on degree theory. Yet small s these solutions are proved to have a square.wave shape, and are re~ated to periodic points o] the mapping ]: R ~ R. When f is not monotone the convergence o] x(t) to the square-wave typically is not uni]orm, and resembles the Gibbs phenomenon o] t~ourier series. (o.:t)~ ~(t) =-x(t) +/(z(t-1… CONTINUE READING

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